Shamik Dasgupta (University of California, Berkeley) - What are we doing when we use abstract entities like numbers or vectors to represent physical quantities like mass or acceleration? There has been considerable work on the *mathematics* of measurement, the task of stating representation and uniqueness theorems that describe conditions under which a quantity can be represented and the ways in which the representation can be transformed. But there has been less work on the *metaphysics* of measurement, the question of what underwrites our talk when we say that x is 5 kgs, for example, or that y is accelerating at 10 m/s^2 in a certain direction. Here I motivate and defend a non-factualist account of this talk. The function of this talk is not to *describe* x or y as being a certain way—in particular, its function is not to describe how they’re related to familiar “standard objects” (*contra* Wittgenstein), nor to attribute them a property that's picked out via these standard objects (*contra* Kripke). Rather, its function is to *cohere* with other statements in one’s linguistic community. Thus, “x is 5 kgs” fulfills its function, and is hence the right thing to say, to the extent that x is half as massive as things that others have called "10 kgs." a quarter as massive as things that others have called "20 kgs," and so on. I then explore the implications of this view regarding the grounds, or metaphysical explanation, of this talk. One implication is that there is no metaphysical explanation of why x is 5 kgs, yet there is a metaphysical explanation of why “x is 5 kg” is the right thing to say: it’s because it coheres with what others in in one’s linguistic community have said. Finally, I show that these implications about metaphysical explanation have significant ramifications for how we interpret initial value problems and the concept of determinism. Roughly, theories that might be thought to be indeterministic turn out to behave in entirely deterministic ways.
